Single-Ended Line Test (SELT) or Double-Ended Line Test (DELT) (known as Loop Diagnostics in some Digital Subscriber Line (DSL) standards), can be used to determine characteristics such as attenuation of a telecommunication transmission line. SELT is typically performed from a DSL Access Multiplexer (DSLAM) in the Central Office (CO). Together with knowledge about transmitter and noise power spectral densities (PSDs), an accurate estimate of attenuation can be used to determine line capacity. An advantage of using SELT to determine attenuation is that there is no need for installation of Customer Premises Equipment (CPE). Thus, it is usable as a tool for service pre-qualification. However, in order to determine line capacity accurately in e.g. a DSL system, attenuation per frequency must be known.
Another application where attenuation versus frequency is required is in order to perform so called Upstream Power Back Off (UPBO) for VDSL2. UPBO means that the CPEs adapt their transmitted signal so that the received power spectral density at the DSLAM is constant, independent of loop length. This requires a method to calculate the attenuation for all frequencies of interest, given only a limited amount of information. For UPBO, it is assumed that attenuation can be described sufficiently as a constant times the square root of frequency.
In certain applications, attenuation is measured or given at one or more frequencies but in order to determine line capacity it may be needed to know attenuation for other frequencies.
Several methods of determining attenuation per frequency are based either explicitly or implicitly on effective resistance per frequency. Prior art in the area of determining attenuation per frequency is based on the following approaches:                Double-Ended Line Test Methods, e.g. Loop Diagnostics as mentioned previously where attenuation is determined by measurement at all frequencies of interest.        Utilization of the fact that for sufficiently high frequencies, attenuation in cables with negligible dielectric losses can be described as a constant times the square root of frequency since effective resistance is proportional to the square root of frequency for these frequencies.        Calibration of Time-Domain Reflectometry (TDR) far-end reflection magnitude against two or more reference cables with known properties and storing calibration vectors consisting of one attenuation value per frequency of interest.        Successive Loop Topology identification, fitting a low-order cable model to each identified loop segment, followed by calculation of attenuation using the cascaded cable models. Such calculation of attenuation often involves calculation of effective resistance, based on two or more parameters.        Calculation of insertion loss using knowledge of the cables, e.g. from operator's databases, together with suitable cable models for the cables in the databases. Such databases could include e.g. the type of cable and the length of each cable segment similar to the result of successive loop topology identification. The cable models could be similar to those used in loop topology identification.        
For xDSL applications, the prior art of calculating attenuation versus frequency as a constant times the square root of frequency (e.g. as for UPBO) works reasonably well for frequencies above a couple of 100 kHz, (i.e. the majority of frequencies used in xDSL systems) but can be inaccurate for lower frequencies (e.g. ADSL upstream, VDSL2 upstream band zero (USO)) since effective resistance is not necessary proportional to the square root of frequency at those frequencies. According to the VDSL2 standard, usage of the previously mentioned UPBO mechanism for USO is an item for further study. It is likely that a more accurate method to determine attenuation would be needed for that purpose.
The approach of calibrating the TDR far-end reflection magnitude requires calibration against two or more reference cables for all frequencies of interest. It also requires storing both the calibration coefficients and the resulting attenuation values for every frequency of interest.
The approach of Successive Loop Topology identification takes the loop topology into account, including effects of standing waves between cable segments with dissimilar impedance. However, this method requires access to the complex-valued input impedance of the loop for a number of frequencies. It also requires significant processing in order to reach the result.
The prior art of using cable models in order to calculate e.g. attenuation require four or more parameters to describe a cable segment apart from the segment length. At least two individual parameters of the four or more parameters are used to describe the frequency dependent resistance i.e. the effective resistance. Typically this includes a DC resistance and a breakpoint frequency where the so called skin effect and the proximity effect become significant.